Observational constraints on the orbit and location of Planet Nine in the outer solar system

No useful constraint on the orbit or position can be drawn from the Malhotra et al. (2016) method.

“Thus, it appears that no useful constraint on the orbit or position can be drawn from this method.”

• cites Malhotra et al. (2016) sourceDisputed

  Section 2.1 concludes that a possible planet orbit plane has an inclination near 48° and longitude of ascending node near −5°. Section 2.3 also estimates that approximately half of the ecliptic longitudes are excluded for the planet’s current location. These are conditional constraints, but they contradict the claim that the method yields no useful constraint on orbit or position. (LLM, conf=0.90)

  Checked by a reasoning model — may be wrong.

  Experimental — accuracy not yet measured

The combined probability of the perihelion clustering and orbital-plane clustering happening due to chance is less than 0.01%.

“The combined probability of these two occurrences happening simply due to chance is less than 0.01%.”

• cites Batygin & Brown (2016) sourcePartly supported

  Section 2, “Orbital Element Analysis” (page not provided), reports that perihelion clustering occurs by chance 0.7% of the time and also identifies orbital-pole clustering. The available body-text passage stops before giving a combined probability, so it does not establish the claimed less-than-0.01% figure. The abstract gives 0.007%, but the audit instructions exclude it as evidence. (LLM, conf=0.78)

  Experimental — accuracy not yet measured

A large perturbing mass either is or was present in the outer solar system at some time.

“Since the time of the discovery of Sedna, it has been clear that a large perturbing mass either is or was present in the outer solar system at some time (Brown et al. 2004).”

• cites Brown et al. 2004 sourcePartly supported

  Section 4 (Origin) says Sedna’s orbit requires perturbation by an unseen planet or forces beyond the solar system. Section 4.1 describes an Earth-mass planet as a possibility but deems it unlikely, while section 4.3 favors early stellar-cluster encounters. The paper therefore supports the need for a perturbation, but not the assertion that a large perturbing mass was necessarily present in the outer solar system. (LLM, conf=0.82)

  Experimental — accuracy not yet measured

Fortney et al. (2016) find a quite high albedo value of 0.75 primarily due to Rayleigh scattering in the atmosphere.

“In addition Fortney et al. (2016) find a quite high albedo value of 0.75 primarily due to Rayleigh scattering in the atmosphere.”

• cites Fortney et al. (2016) sourcePartly supported

  In Optical Characterization (p. 3), the paper gives 0.75 as the geometric albedo of an infinitely deep Rayleigh-scattering atmosphere, not as an unqualified albedo for Planet Nine. The same section says Raman scattering can lower it at UV wavelengths, while clouds can alter it at other wavelengths (pp. 3–4). (LLM, conf=0.87)

  Experimental — accuracy not yet measured

Most wide-field surveys of the Kuiper belt have not been sensitive to sky motions smaller than about 1 arcsecond per hour.

“While most wide-field surveys of the Kuiper belt have not been sensitive to sky motions smaller than about 1 arcsecond per hour (i.e., Millis et al. 2002;Brown 2008;Petit et al. 2011)”

• cites Millis et al. 2002 sourceCould not verify

  Section 2.3 gives a typical apparent motion of 2–3 arcseconds per hour for main-belt Kuiper belt objects near opposition, but that is not a survey sensitivity limit. Sections 2.6 and 3 describe survey exposures and detection methods; neither establishes that most wide-field surveys were insensitive below about 1 arcsecond per hour. Searches for slow-motion detection limits found no supporting passage. (LLM, conf=0.72)

  Experimental — accuracy not yet measured
• cites Brown 2008Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites Petit et al. 2011 sourceSupported

The WISE spacecraft surveyed the entire sky twice in its 3.4 and 4.6 μm bands, allowing Luhman (2014) to rule out Saturn-sized planets out to a distance of ∼30,000 au.

“The WISE spacecraft surveyed the entire sky twice in its 3.4 and 4.6 μm (W1 and W2) bands, allowing Luhman (2014) to rule out Saturn-sized planets-which have substantial enhanced short-wavelength emission owing to emission from internal heat-out to a distance of ∼30,000 au.”

• cites Luhman (2014) sourceSupported

All well-determined orbits of KBOs beyond Neptune with semimajor axis larger than 227 au approach perihelion within 94 degrees of longitude of each other.

“Most importantly, Batygin & Brown (2016) point out that all well-determined orbits of KBOs beyond Neptune with semimajor axis, a, larger than 227 au approach perihelion within 94° of longitude of each other.”

• cites Batygin & Brown (2016) sourcePartly supported

  Section 2 (page unavailable) reports that six KBOs with semimajor axes greater than 250 AU reach perihelion at longitudes between 20° and 130°, supporting the general claim of clustering. It does not give the cited cutoff of 227 AU or a 94° longitude span; its reported span is 110°. (LLM, conf=0.88)

  Experimental — accuracy not yet measured

The numerical setup using direct N-body perturbations for Planet Nine and Neptune and an enhanced quadrupolar field for the remaining giant planets successfully captures the relevant dynamical phenomena at reduced computational cost.

“As shown in Batygin & Brown (2016), such a numerical setup successfully captures the relevant dynamical phenomena, at a substantially reduced computational cost.”

• cites Batygin & Brown (2016) sourcePartly supported

  Section 4 (page unavailable) says the simulations treated the distant companion directly and the giant planets through an enhanced quadrupolar field, successfully capturing their secular perihelion advance. But Section 5.1 (page unavailable) says the later simulations treated all planetary perturbations directly. Our copy does not establish the claimed setup with Neptune direct and the remaining giants represented by a quadrupole, or a substantial reduction in computational cost. (LLM, conf=0.88)

  Experimental — accuracy not yet measured

Dynamical sculpting of a planetesimal population yields a configuration where long-term stable objects have longitudes of ascending node roughly equal to that of Planet Nine.

“As demonstrated by Batygin & Brown (2016), dynamical sculpting of such a planetesimal population yields a configuration where long-term stable objects have longitudes of ascending node roughly equal to that of Planet Nine.”

• cites Batygin & Brown (2016) sourceSupported

These KBOs share very nearly the same orbital plane, tilted an average of 22 degrees to the ecliptic.

“Moreover, these objects also share very nearly the same orbital plane, which is tilted an average of 22° to the ecliptic.”

• cites Batygin & Brown (2016) sourcePartly supported

  Section 2 (page not provided) reports that the distant KBOs’ orbits are physically aligned and that their orbital poles cluster, supporting the claim that they share nearly the same plane. Our copy does not give an average tilt of 22° to the ecliptic, so the numerical part is not supported. (LLM, conf=0.86)

  Experimental — accuracy not yet measured

The clustering, when combined with the clustering in pole angle, was unexpected at the 99.993% confidence level.

“Batygin & Brown (2016) showed that this clustering, when combined with the clustering in pole angle, was unexpected at the 99.993% confidence level.”

• cites Batygin & Brown (2016) sourceSupported

The Luhman (2014) results provide no constraints on the position or existence of Planet Nine.

“The Luhman (2014) results thus provide no constraints on the position or existence of Planet Nine.”

• cites Luhman (2014) sourceCould not verify

  Section 7, “Constraints on a Solar Companion” (page unavailable), gives WISE detection limits for Saturn- and Jupiter-like objects and says the results constrain brown dwarfs and large gas giants. Our copy does not discuss Planet Nine or establish whether those limits apply to its position or existence; searches for Planet Nine and lower-mass-planet constraints found no decisive passage. (LLM, conf=0.73)

  Experimental — accuracy not yet measured

Planet Nine near perihelion would cause such a large effect on the Earth-Saturn distance that the Fienga et al. (2016) analysis and an extension by Holman & Payne (2016) can rule out any of the Planet Nine solutions near perihelion over the range of R.A. > 255° and R.A. < 2°.

“At its the nearest possible locations, in particular, Planet Nine would cause such a large effect on the Earth-Saturn distance that the Fienga et al. (2016) analysis and an extension by Holman & Payne (2016) (which assumes the same residuals) can rule out any of the Planet Nine solutions near perihelion over the range of R.A. of R.A. > 255 9 , R.A. < 2 9 deg.”

• cites Fienga et al. (2016) sourcePartly supported

  Split into 2 atoms — 1 confirmed, 1 partially supported, 0 disputed, 0 misattributed, 0 unverifiable. Expand the claim to see per-atom verdicts.

  Experimental — accuracy not yet measured
• cites Holman & Payne (2016) sourcePartly supported

  Split into 2 atoms — 1 confirmed, 1 partially supported, 0 disputed, 0 misattributed, 0 unverifiable. Expand the claim to see per-atom verdicts.

  Experimental — accuracy not yet measured

• AssumptionThe authors state this as an assumption: The signal apparently detected by Fienga et al. (2016) is at or near the level of systematic errors in this type of analysis, and larger signals from Planet Nine could be detected.

Fienga et al. (2016) perform full fits to the locations of all planets and nearly 300 asteroids with and without a 10 M_e Planet Nine at various positions along an orbit with a=700 au and e=0.6.

“Fienga et al. (2016)perform full fits to the locations of all planets and nearly 300 asteroids observed from ancient times to the present with and without a 10 M e Planet Nine at various positions along an orbit with = a 700 au 9 and e 9 = 0.6, consistent with the nominal orbit suggested in Batygin & Brown (2016).”

• cites Fienga et al. (2016) sourcePartly supported

  Sections 2 and 3.2 describe global fits of planetary orbits with and without a 10-Earth-mass Planet Nine at positions sampled around its proposed orbit; the Abstract gives a = 700 AU and e = 0.6. Section 3.1 says the model takes up to 298 asteroids into account, but it does not say the authors fitted those asteroids’ locations. The fits described in Section 3.2 are of planetary-orbit parameters. (LLM, conf=0.87)

  Experimental — accuracy not yet measured

Only a narrow range of Planet Nine orbital elements can reproduce the observed aligned eccentric high semimajor axis KBO population.

“We find that only a narrow range of orbital elements can reproduce the observations.”

Orbitally confined KBOs generally have orbital planes similar to that of Planet Nine.

“Orbitally confined objects also generally have orbital planes similar to that of the planet, suggesting that the planet is inclined approximately 30°to the ecliptic.”

Comparison of allowed orbital positions and estimated brightness of Planet Nine to previous and ongoing surveys rules out approximately two-thirds of the planet's orbit.

“We compare the allowed orbital positions and estimated brightness of Planet Nine to previous and ongoing surveys which would be sensitive to the planet's detection and use these surveys to rule out approximately two-thirds of the planet's orbit.”

The combination of semimajor axis, eccentricity, and mass of Planet Nine strongly dictates the semimajor axis range of the orbital confinement of the distant eccentric KBOs.

“In particular, the combination of semimajor axis, eccentricity, and mass of Planet Nine strongly dictates the semimajor axis range of the orbital confinement of the distant eccentric KBOs.”

In the simulation with Planet Nine mass 10 Earth masses, semimajor axis 500 au, and eccentricity 0.6, from 200 to 600 au the longitudes are confined around 180 degrees, anti-aligned with Planet Nine.

“From 200 to 600 au the longitudes are confined around 180°, that is, they are anti-aligned with Planet Nine.”

The seven KBOs with semimajor axis larger than 227 au cluster within 94 degrees of perihelion longitude.

“The seven objects with > a 227 au cluster within 94° of perihelion longitude.”

For the 10 Earth-mass simulations, all simulations that cannot be excluded at the 99% confidence level fall within a semimajor axis range of 500 to 800 au approximately along an empirically defined line in eccentricity versus semimajor axis.

“In general, all simulations that cannot be excluded at at the 99% confidence level fall with a range of = a 500, 800 9 [ ] au approximately along an empircally defined line of = e a 0.75 450 au 9 9 8 ( ), shown as the dashed line in Figure 2.”

From 100 to 200 au, 13 KBOs are loosely clustered within 223 degrees of each other.

“While KBOs with semimajor axes out to 100 au appear randomly distributed in longitude, from 100 to 200 au, 13 objects are loosely clustered within 223° of each other.”

The 0.1, 1, and 30 Earth-mass simulations have no acceptable solutions.

“Figures 2 and 3 show grids of probabilities for the 10 and 20 M e simulations (the 0.1, 1, and 30 M e simulations have no acceptable solutions).”

The five known high-inclination objects in the outer solar system with a > 200 au and i > 50° are all Centaurs with perihelion distances between 8 and 15 au.

“the five high inclination objects are all Centaurs with < < q 8 1 5a u .”

Neptune is detected 16 times with a signal-to-noise of approximately 50 in the W1 band.

“Neptune is detected 16 times with a signal-to-noise (S/N) of approximately 50 in the W1 band.”

The lack of high perihelion objects between 100 and 200 au strongly rules out all low semimajor axes and nearly all highest eccentricities.

“The lack of high perihelion objects between < < a 100 200 au strongly rules out all of the low semimajor axes and nearly all of the highest eccentricities, while the need to confine objects in perihelion longitude requires moderately high eccentricities or moderately low semimajor axes.”

The combined effect of the two constraints makes for a rather narrow combination of Planet Nine semimajor axis versus eccentricity with acceptable solutions.

“The combined effect of these two constraints makes for a rather narrow combination of a 9 versus e 9 with acceptable solutions.”

Such acceptable 10 Earth-mass orbits have a Planet Nine perihelion in the range of approximately 200 to 340 au.

“Such orbits have a perihelion, q 9 , in the range ~200, 340 [ ] au.”

The clustering in perihelion location and pole angle is clearly visible for objects with q greater than 30 au and a greater than 60 au.

“The clustering in perihelion location as well as pole angle is clearly visible.”

The confinement efficiency drops smoothly until, at an inclination of 60 degrees and higher, it scatters around 20%.

“The confinement efficiency drops smoothly until, at an inclination of 60° and higher, it scatters around 20%.”

In simulations with good confinement in longitude, the polar angles of the simulated orbits are approximately perpendicular to the plane of Planet Nine, particularly for objects that come to perihelion in the plane of the planet.

“perpendicular to the plane of Planet Nine, particularly for objects that come to perihelion in the plane of the planet.”

Higher-mass simulations cannot match the observations at all.

“Higher-mass simulations cannot match the observations at all.”

Assuming all WISE images are coadded, Neptune could be detected with an S/N of 10 only to ∼63 au, consistent with the estimate above.

“Assuming that all of those images are coadded, Neptune could be detected with an S/N of 10 only to ∼63 au, consistent with our estimate above.”

• AssumptionThe authors state this as an assumption: All WISE images of Neptune are coadded.

Almost all simulations can be ruled out at greater than the 99% confidence level.

“Almost all simulations can be ruled out at greater than the 99% confidence level.”

The efficiency of confinement of the distant population drops dramatically with increased inclination of Planet Nine.

“Upon examination of these simulations, we find that efficiency of confinement of the distant population drops dramatically with increased inclination of Planet Nine.”

The seven aligned distant KBOs have a large value and tight confinement in pole angle, 22 degrees plus or minus 6 degrees.

“One of the striking characteristics of the seven aligned distant KBOs is the large value of and tight confinement in the pole angle (22° ± 6°; Figure 1).”

The planar simulations provide no constraints on inclination, argument of perihelion, or longitude of ascending node of Planet Nine.

“The planar simulations provide no constraints on inclination, i 9 , argument of perihelion w 9 , or longitude of ascending node, W 9 , of Planet Nine.”

There is a systematic trend in the simulations where objects with smaller perihelion distances move to the outer edge of the clustering regions, just like the real low perihelion objects appear to be.

“we note a systematic trend where objects with smaller perihelion distances move to the outer edge of the clustering regions, just like the real low perihelion objects appear to be.”

The probability of such a loose clustering of 13 objects occurring in randomly distributed data is smaller than 5%.

“While this clustering is not as visually striking, the probability of such a loose clustering of 13 objects occurring in randomly distributed data is smaller than 5%.”

The Planet Nine orbits produced by these assumptions do not produce the spatial confinements of the KBOs that are observed.

“Not surprisingly, the Planet Nine orbits produced by these assumptions do not produce the spatial confinements of the KBOs that are observed.”

No particular preference for type of critical angle or even resonance order can be identified in the dynamical simulations shown here.

“Indeed, no particular preference for type of critical angle or even resonance order can be identified in the dynamical simulations shown here.”

As of 2016 May 15, no series of transients can be found that fit an outer solar system body on any bound Keplerian orbit in the PST data.

“As of 2016 May 15, no series of transients can be found that fit an outer solar system body on any bound Keplerian orbit.”

The CRTS survey was determined to be essentially 100% complete to V∼19.1 in the north and V∼18.6 in the south.

“The survey was determined to be essentially 100% complete to Ṽ 19.1 in the north and Ṽ 18.6 in the south.”

Every bright KBO in the survey fields was detected, often dozens of times.

“Every bright KBO in the survey fields was detected, often dozens of times.”

Planet Nine is inclined approximately 30 degrees to the ecliptic.

“Orbitally confined objects also generally have orbital planes similar to that of the planet, suggesting that the planet is inclined approximately 30°to the ecliptic.”

Planet Nine is likely near aphelion.

“Planet Nine is likely near aphelion with an approximate brightness of < < V 22 2 5 .”

The perihelion longitude of Planet Nine is fixed at 241° ± 15°.

“We fix the perihelion longitude at 241° ± 15°.”

A few surveys have had the sensitivity and cadence to have potentially detected Planet Nine at some point in its orbit.

“a few surveys have had the sensitivity and cadence to have potentially detected Planet Nine at some point in its orbit.”

One strong prediction of the existence of a giant planet in the outer solar system is that it will cause Kozai-Lidov oscillations that drive modest inclination objects onto high inclination perpendicular and even retrograde orbits and then back again.

“One strong prediction of the existence of a giant planet in the outer solar system is that it will cause Kozai-Lidov oscillations that will drive modest inclination objects onto high inclination perpendicular and even retrograde orbits and then back again.”

A 10 M_e planet would not be expected to have enhanced short-wavelength emission.

“A 10 M e planet, however, would not be expected to have this enhanced shortwavelength emission.”

The semimajor axis at which anti-alignment begins and the range where broad confinement is evident are strong indicators of the combination of semimajor axis and eccentricity of Planet Nine.

“The semimajor axis at which anti-alignment begins and the range where broad confinement is evident are strong indicators of the combination of semimajor axis and the eccentricity of Planet Nine.”

The existence of Planet Nine predicts a collection of high semimajor axis eccentric objects with inclinations essentially perpendicular to the rest of the solar system.

“Additionally, the existence of Planet Nine predicts a collection of high semimajor axis eccentric objects with inclinations essentially perpendicular to the rest of the solar system.”

To transform the mass of Planet Nine into an expected brightness requires assumptions of both radius (and thus composition) and albedo (and thus surface composition), neither of which is constrained by any of the observations.

“To transform this mass into an expected brightness requires assumptions of both radius (and thus composition) and albedo (and thus surface composition), neither of which is constrained by any of our observations.”

This ties together Planet Nine argument of perihelion and longitude of ascending node through a fixed longitude of perihelion.

“In turn, this ties together w 9 and W 9 through a fixed longitude of perihelion (which is the sum of these parameters).”

The perihelion locations of the perpendicular high semimajor axis Centaurs effectively rule out the possible higher inclination orbits for Planet Nine.

“The perihelion locations of the perpendicular high semimajor axis Centaurs effectively rule out the possible higher inclination orbits for Planet Nine.”

The loose clustering of smaller semimajor axis objects can be explained as a consequence of some orbital configurations of Planet Nine.

“As will be seen, such a loose clustering of smaller semimajor axis objects can indeed be explained as a consequence of some orbital configurations of Planet Nine.”

The clustered objects are along the same orbit plane as Planet Nine.

“confirming our observation that the clustered objects are along the same orbit plane as the planet.”

Substantial uncertainty comes not just from the statistics of the objects themselves, but from the currently small number of simulations in the best-fit region of parameter space.

“substantial uncertainty comes not just from the statistics of the objects themselves, but from the currently small number of simulations in the best-fit region of parameter space.”

For inclinations of 30 degrees, the allowable range for Planet Nine argument of perihelion appears to be approximately 120 to 160 degrees.

“For inclinations of 30°, the allowable range for the argument of perihelion appears to be w 9 ∼ 120°-160°.”

The prediction of perpendicular high semimajor axis eccentric objects is strongly supported by the collection of low perihelion Centaurs with perpendicular orbits whose origin had previously been mysterious.

“Unexpectedly, this prediction is strongly supported by the collection of low perihelion Centaurs with perpendicular orbits whose origin had previously been mysterious (Gomes et al. 2015).”

• cites Gomes et al. 2015 sourceNot checked — no full text of the source

The acceptable range is sufficiently narrow that the grid spacing of the simulations is often too large to capture acceptable solutions at all semimajor axes or eccentricities.

“In fact, the range is sufficiently narrow that it is clear that the grid spacing of our simulations is often too large to capture acceptable solutions at all semimajor axes or eccentricities.”

For inclinations of approximately 22 degrees, Planet Nine argument of perihelion must be quite close to 150 degrees.

“For inclinations of ∼22°, ω must be quite close to 150°.”

These results suggest, but do not demand, that Planet Nine has only a modest inclination.

“These results suggest, but do not demand, that Planet Nine has only a modest inclination.”

The existence of Planet Nine can be ruled out over about two-thirds of its orbit.

“The existence of Planet Nine can be ruled out over about two-thirds of its orbit.”

The assumption of simple low-order resonance is thus unlikely to be justified.

“The assumption of simple low-order resonance is thus unlikely to be justified.”

More recent fits, leading to the creation of the DE435 JPL planetary ephemeris, put even tighter constraints on any remaining residuals.

“while even more recent fits, leading to the creation of the DE435 JPL planetary ephemeris, put even tighter constraints on any remaining residuals.”

The VISTA surveys and Subaru Hyper-Suprime Cam survey do not overlap with the required search region.

“The large community surveys that are concentrating on specific areas of the sky, such as the VISTA surveys in the southern hemisphere and the Subaru Hyper-Suprime Cam survey along the celestial equator unfortunately do not overlap with the required search region.”

Detection of high semimajor axis perpendicular objects has the strong possibility of entirely ruling out the existence of Planet Nine if they are not found with perihelia in the locations predicted by the hypothesis.

“detection of these objects also has the strong possibility of entirely ruling out the existence of Planet Nine if they are not found with perihelia in the locations predicted by the hypothesis.”

At present, the statistical reliability of the constraints is limited as much by the limited survey nature of the simulations as by the small number of observed objects themselves.

“At present, the statistical reliability of our constraints are limited as much by the limited survey nature of the simulations as by the small number of observed objects themselves.”

Such an object would be well within the limits of 10 m class telescopes.

“While faint, such an object would be well within the limits of 10 m class telescopes.”

The perihelion locations and values of ω of high semimajor axis perpendicular objects change strongly with w9 and i9 and so can be used to better refine estimates of these parameters.

“their perihelion locations and values of ω change strongly with w 9 and i 9 and so can be used to better refine these estimates.”

If the sensitivity estimates are correct, the Pan-STARRS 1 moving object survey has or will rule out a substantial fraction of the non-aphelion sky.

“If these sensitivity estimates are correct, the Pan-STARRS 1 moving object survey has or will rule out a substantial fraction of the non-aphelion sky.”

The DES data will be sensitive to Planet Nine if it is in the survey area.

“it is clear that the data will be sensitive to Planet Nine if it is in the survey area.”

The Keplerian filter is strong.

“The Keplerian filter is strong.”

At its most distant allowed location and with a Neptune-like albedo, a 20 R_e Planet Nine is approximately V=25.

“At its most distant allowed location and with a Neptune-like albedo, a 20 R e Planet Nine is approximately V = 25.”

The DES team estimates a Planet Nine detection limit of r=23.8.

“The DES team estimates a Planet Nine detection limit of r 23.8 (D.Gerdes 2016, private communication).”

• cites D.Gerdes 2016, private communicationNot matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

The sensitivity of the WISE data to Neptune-sized planets except at the closest possible distances remains low.

“the sensitivity of the WISE data to Neptune-sized planets except at the closest possible distances remains low.”

The PST survey rules out much of the sky within about 45° of the predicted perihelion point, with the exception of the region near the galactic plane.

“This survey rules out much of the sky within about 45° of the predicted perihelion point, with the exception of the region near the galactic plane.”